Three-dimensional Josephson-junction arrays in the quantum regime

TL;DR

This paper investigates the quantum phase transitions in a 3D array of Josephson junctions, employing a novel algebraic approach and mapping to a quantum spherical model to analyze phase diagrams and fluctuation conductivity.

Contribution

It introduces a quantum algebraic framework for 3D Josephson arrays and maps the problem onto a solvable quantum spherical model, providing new insights into their phase transitions.

Findings

Phase diagram as a function of temperature, Josephson coupling, and charging energy.

Universal scaling form of fluctuation conductivity near the quantum critical point.

Identification of quantum critical behavior in 3D Josephson junction arrays.

Abstract

We study the quantum phase transition properties of a three-dimensional periodic array of Josephson junctions with charging energy that includes both the self and mutual junction capacitances. We use the phase fluctuation algebra between number and phase operators, given by the Euclidean group E_2, and we effectively map the problem onto a solvable quantum generalization of the spherical model. We obtain a phase diagram as a function of temperature, Josephson coupling and charging energy. We also analyze the corresponding fluctuation conductivity and its universal scaling form in the vicinity of the zero-temperature quantum critical point.